Solve (5-2)² - 2³: Order of Operations with Squares and Cubes

Q: Why do parentheses come before exponents in PEMDAS?

Parentheses always have the highest priority because they group operations together. In $ (5-2)^2 $, you must find what's inside the parentheses first (3), then apply the exponent.

Q: What's the difference between 2³ and 3²?

$ 2^3 = 2 × 2 × 2 = 8 $ (2 multiplied by itself 3 times) while $ 3^2 = 3 × 3 = 9 $ (3 multiplied by itself 2 times). The base number and exponent both matter!

Q: Can I work from left to right instead of using PEMDAS?

No! Working left to right ignores the order of operations and gives wrong answers. For example, doing 5-2² first would give you 3², but 2³ should be calculated as 8 separately.

Q: How do I remember which exponent calculations to do first?

Handle all parentheses first, then calculate all exponents (both $ (5-2)^2 $ and $ 2^3 $), then do the subtraction. Think: group, power, subtract!

Q: What if I get a different answer like 6 or 8?

Check your work! Getting 6 usually means you calculated $ 3^2 - 2 = 9 - 2 = 7 $ instead of $ 2^3 = 8 $. Getting 8 means you forgot to subtract: $ 9 - 8 = 1 $, not just 8.

Exponent Evaluation with Parentheses

Calculate and indicate the answer:

$(5-2)^2-2^3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Always solve the parentheses first

00:10 An exponent is actually the number multiplied by itself as many times as the power

00:12 Break down each exponent into multiplications and solve

00:21 Substitute the solutions into our question and calculate

00:27 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate and indicate the answer:

$(5-2)^2-2^3$

Step-by-step solution

Remember that according to the order of arithmetic operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms with exponents and then subtract the results:

$(5-2)^2-2^3 =3^2-2^3=9-8=1$ Therefore, the correct answer is option C.

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then exponents, before subtraction
Technique: Calculate $(5-2)^2 = 3^2 = 9$ and $2^3 = 8$ separately
Check: Substitute back: 9 - 8 = 1 matches our answer ✓

Common Mistakes

Avoid these frequent errors

Calculating exponents before parentheses
Don't calculate 2³ = 8 first and then (5-2)² = wrong order! This violates PEMDAS and leads to confusion about which operations to do when. Always complete parentheses first, then handle all exponents, then subtract.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do parentheses come before exponents in PEMDAS?

Parentheses always have the highest priority because they group operations together. In $(5-2)^2$ , you must find what's inside the parentheses first (3), then apply the exponent.

What's the difference between 2³ and 3²?

$2^3 = 2 × 2 × 2 = 8$ (2 multiplied by itself 3 times) while $3^2 = 3 × 3 = 9$ (3 multiplied by itself 2 times). The base number and exponent both matter!

Can I work from left to right instead of using PEMDAS?

No! Working left to right ignores the order of operations and gives wrong answers. For example, doing 5-2² first would give you 3², but 2³ should be calculated as 8 separately.

How do I remember which exponent calculations to do first?

Handle all parentheses first, then calculate all exponents (both $(5-2)^2$ and $2^3$ ), then do the subtraction. Think: group, power, subtract!

What if I get a different answer like 6 or 8?

Check your work! Getting 6 usually means you calculated $3^2 - 2 = 9 - 2 = 7$ instead of $2^3 = 8$ . Getting 8 means you forgot to subtract: $9 - 8 = 1$ , not just 8.

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Solve (5-2)² - 2³: Order of Operations with Squares and Cubes

Exponent Evaluation with Parentheses

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do parentheses come before exponents in PEMDAS?

What's the difference between 2³ and 3²?

Can I work from left to right instead of using PEMDAS?

How do I remember which exponent calculations to do first?

What if I get a different answer like 6 or 8?

🌟 Unlock Your Math Potential

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